As Baghdad awaits Barack Obama's decision on air strikes against the jihadist army conquering much of Iraq, the senior US military officer suggested that the US still lacks sufficient intelligence to take action.

Army general Martin Dempsey, chairman of the joint chiefs of staff, told a Senate panel on Wednesday that "until we can clarify this intelligence picture" the US would have difficulty knowing who it would be attacking from the air, indicating military as well as political reluctance to any return to the skies above Iraq.

"It's not as easy as looking at an iPhone video of a convoy and then striking it," Dempsey told a Senate appropriations subcommittee as he and defense secretary Chuck Hagel focused far more on the limits of what the US can accomplish in Iraq than the possibilities. Both sounded far less urgent than Iraqi leaders.

Dempsey, who once commanded the training of the Iraqi military and police, cited the case of an Iraqi army facility in Mosul falling first to the Islamic State in Iraq and the Levant (Isis) and then to the Kurdish peshmerga quasi-army within a 36-hour timeframe, raising doubts about the ability of the US air force or navy aviators to sufficiently know who they would be striking by the time of their arrival.

The murky picture, exacerbated by the relative paucity of US intelligence sources on the ground in Iraq, comes despite Dempsey's description of the US moving what he described as "a great deal of manned and unmanned ISR to gain clarity", using a military term for intelligence, surveillance and reconnaissance planes and other tools.

But Dempsey confirmed for the first time that Iraq had indeed sent the US requests for air power to stanch the advance of Isis, which has taken several cities over the past week throughout Sunni Iraq.

"We have a request from the Iraqi government for air power," Dempsey told senator Lindsey Graham, Republican of South Carolina.

Reuters reported that US officials, speaking on condition of anonymity, said that Iraq's request had included a call for drone strikes and increased surveillance by US drones, which have been flying over Iraq for some time. The Pentagon has said it stepped up surveillance, intelligence and reconnaissance efforts, at Baghdad's request.

The formal air power request complicates Obama's decision-making. While Obama administration officials have spent the past three days emphasizing what they are calling a comprehensive consideration of aid for the Iraq crisis – broader, they say, than a military strike – the request places Obama in the position of potentially rebuking a partner, however much a frustrating one, in a moment of extreme need.

Yet Dempsey and Hagel excoriated the government of Nouri al-Maliki during the Senate hearing, at times sounding like it was more to blame than Isis for Iraq's imperiled future.

Both lowered expectations about what benefits US can actually bring to Iraq, and sharply rebuked suggestions that the US is responsible for the crisis. Neither even remotely endorsed returning to military action in Iraq, from the air or otherwise, a significant omission from two of Obama's most important defense officials.

Asked if the consideration of a military response comes too late to stop Isis, Dempsey said: "It's only late if you suggest we could have stopped it. … There is very little that could have been done to overcome the degree to which the government of Iraq has failed its people. That is what has caused this problem."

Dempsey, saying he was speaking as an Iraq veteran, expressed "bitter disappointment" with what he called a failed Iraqi government.

Hagel, reiterating a theme of his perspective on foreign affairs both as a senator and at the Pentagon, repeatedly emphasized that the US "can't dictate outcomes. It's up to the Iraqi people." Both he and Dempsey acknowledged that there was a possibility that Afghanistan could follow Iraq into chaos after the US leaves in 2016, but downplayed the possibility.

Admonishing Senator Graham, a longtime opponent of the 2011 military pullout compelled by the Iraqi government, Hagel replied: "We didn't lose anything. It wasn't the United States that lost anything. … We have done everything we could to help them, but it's up to the Iraqis."

It was a theme repeatead at the White House later, where spokesman Jay Carney said Maliki had not done enough "to govern inclusively and that has contributed to the situation and the crisis that we have today in Iraq."

He stopped short of calling for Maliki - in power for eight years and the effective winner of a parliamentary election two months ago - to resign. Asked if Maliki should step down, Carney told reporters: "That's not, obviously, for us to decide."

Speaking in the Senate, Republican hawk John McCain called for the use of American air power, but also urged Obama to "make it make very clear to Maliki that his time is up." The Obama administration has not openly sought Maliki's departure, but has shown signs of frustration with him.

Obama briefed congressional leaders later on Wednesday. Speaking afterwards, House minority leader Nancy Pelosi said the White House meeting had been "very informative" but said Obama did not specify an action plans, focusing instead on his perspective of what was happening Iraq.

Various and conflicting reports ahead of the White House meeting indicated a lack of clarity around the scope, mission and timing about potential air strikes, some citing the difficulties indicated by Dempsey about clear targeting. Veterans of air campaigns told the Guardian that time is unlikely to yield clarity as Isis intermingles with civilians in Iraqi cities, raising questions about what the US can accomplish.

Dempsey, who favored a residual US force in Iraq in 2011, told the Senate hearing that Isis had "aspirations to attack western interests" and said "not at this time but over time" the group could threaten the US homeland.